This paper concerns the tracking of automotive radar targets by a radar using a high-resolution 2D spectral estimator in order to detect the radar targets. We show how to implement the tracking, discuss the measurement variances, and show how we can exploit the high resolution in order to make a better tracking filter. Existing automotive radar systems are affected by a limited field of view, poor angular accuracy, or low measurement update rate. By using a combination of a waveform solving, the target ambiguity problem within a short measurement time and a conformal array design, we eliminate these problems and by the use of the 2D APES estimator, we achieve a high angular resolution, which is used in order to improve the tracking. The simulation results show that we are able to track a laterally moving vehicle very accurately and that the new improved tracking filter achieves more robust and accurate tracking along with a short initialization time. These attributes can be very important for safety critical applications.